You won’t see any app on his laptop because he’s viewing and managing it from the internet browser by remotely connecting to the Router through an internet browser.

So no he’s not bluffing, incognito might hide the history for others using your PC but all that info still passes through the router and it is viewable by ISP and router admin. And even if he wasn’t viewing the router he could easily just ask the ISP for a report on what sites are being visited on your network.

So yeah your dad knows what porn sites you’re visiting.

I could say you could get around this by using your phone’s data connection but he’s likely paying for that too so he can just ask your Cell Service Provider for what porn sites you visit.